ECON1001/7001
Tutorial Problems/Questions  Week 04
Problem 1
Compute the derivatives of the functions f : R
(1a) f (x) = 3x 8
(1b) f (x) = 3x4 8x + 99
(1c) f (x) = 3x5 2x4 + 8(x2 + x 1) 3
(1d) f (x) = x 2
f0g ! R below.
Problem 2
For each function f : A
Tutorial Solutions: Week 12
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Note: These are only sketches of the solutions. Fully correct solutions require all
working and/or written explanation.
Review problems for chapter 16
Ques
Tutorial Solutions: Week 10
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Note: These are only sketches of the solutions. Fully correct solutions require all
working and/or written explanation.
Review problems for chapter 13
Ques
EMET1001
Foundations of Economic and Financial Models
Week 6: Integration
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Australian National University
Spring 2016
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Week 6
Spring 2016
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Indefinite integrals (9.1)
Example: suppose the marginal cost function of a firm
EMET1001: Foundations of Economic and Financial Models
Practice Questions: Final Exam
October, 2016.
1. Consider the following function
f (x) = x3 2x2 + x
(a) Find the domain of f .
(b) Compute the limit of f as x and x .
(c) Write the first, second and t
EMETlOOl
Foundations of Economic and Financial Models
Week 10: Multivariable optimization
ldione Meneghel
Australian National University
Spring 2016
Meneghel
cfw_ANU)
Week 10
Spring 2016
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Optimization with two variables (13.1)
*
Typical pictures:

EMETlOOl
Foundations of Economic and Financial Models
Week 8: Functions of Many Variables
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Australian National University
Spring 2016
Meneghel (ANU)
Week 8
Spring 2016
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Functions of many variables
*
Before, we had y = f(x).
*
But in o
Practice Questions: Midterm Exam
August 22, 2016.
Note: For the actual exam, you will have a reading period of 15 minutes and a
writing period of 90 minutes.
Question 1
Dierentiate the following functions:
(a) y = 7x4 + 3x3 + 8x 1
2x3 5
(b) y = 5
4x x2 +
EMET1001
Foundations of Economic and Financial Models
Week 4: Implicit Differentiation, Polynomial Approximations and Limits
ldione Meneghel
Australian National University
Spring 2016
Meneghel
cfw_ANU)
Week 4
Spring 2016
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Implicit differentiation
*
EMET1001
Foundations of Economic and Financial Models
Week 5: SingleVariable Optimization
Idione Meneghel
Australian National University
Spring 2016
Meneghel (ANU)
Week 5
Spring 2016
1 / 48
Definition of global extreme points (8.1)
[D] Global extreme poi
Solutions: Midterm Exam
August 30, 2016.
Question 1
Dierentiate the following functions with respect to x:
2
6
(a) y = x4 7x2 +
3
x
(b) y = x3 4
2
(c) y = (x2 + ex )2
(d) y = x3 (ln x)3
8
6
Solution. (a) y = x3 14x 2
3
x
1 3
3x2
12
2
(b) y = (x 4) 3x =
2
EMET1001
Foundations of Economic and Financial Models
Week 8: Functions of Many Variables
Idione Meneghel
Australian National University
Spring 2016
Meneghel (ANU)
Week 8
Spring 2016
1 / 38
Functions of many variables
Before, we had y = f (x).
But in or
EMETlOOl
Foundations of Economic and Financial Models
Week 7: Extra Examples
ldione Meneghel
Australian National University
Spring 2016
Meneghel (ANU)
Week 7
Spring 2016
1 / 15
Graphsketching
1. Domain and intersections with axis
x~o
Meneghel
_.,
0
f'o :
EMET1001
Foundations of Economic and Financial
Models
Course Description
The course teaches the mathematical foundations of models in economics, business and
finance and its applications. Mathematical topics covered include set theory, functions, series,
EMET1001
Foundations of Economic and Financial Models
Week 13: Loose ends and review
ldione Meneghel
Australian National University
Spring 2016
Meneghel
(ANU)
Week 13
Spring 2016
1 / 30
M ultivaria ble Optimization:
Loose Ends
Meneghel
(ANU)
Week 13
Sprin
EMET1001
Foundations of Economic and Financial Models
Week 12: Matrix Algebra
ldione Meneghel
Australian National University
Spring 2016
Meneghel
(ANU)
Week 12
Spring 2016
1 / 24
Systems of linear equations
*
I
Can we solve the system of equations Ax= b?
ECON1001/7001
Tutorial Problems/Questions  Week 03
Problem 1
Read Newtons Binomial Formula and Pascals Triangle in chapter 3.
(1a) Expand (2xy 2 z 1 3x3 y 1 z 2 )6 .
(1b) Find the coe cient of x25 in the expansion of (2x2 y 3 + x=y)20 .
Problem 2
Find th
ECON1001/7001
Tutorial Problems/Questions  Week 02
The solutions will be presented during tutorial sections.
Discussion about Bonus Problems will only occur if time permits.
Problem 1
(1a) Write the mathematical formula of any function that has a graph
m
ECON1001/7001
Tutorial Problems/Questions  Week 08 (2016)
Problem 1
Compute the onesided limits (i.e., the lateral limits), if they exist, or
explain why they do not exist.
lim
x!0+
lim
x!0+
lim
x!0
x2 + 1
+ 2x
x
x(x2 + 7)
jxj
x(x2 7)
jxj
Problem 2
Cons
ECON1001/7001
Tutorial Problems/Questions  Week 06 (2016)
Problem 1
Compute the rst and second derivatives of the functions f : (0; +1) !
R below.
(1a) f (x) = 3x9 8x 0:5
(1b) f (x) = 7
1
(1c) f (x) = g(x)h(x), where g : (0; +1) ! R and h : (0; +1) ! R a
Week 2:
Demand and inverse demand
As the price P belongs to R+, increases, the aggregate demand Q belongs to R+, goes down P and
Q move in opposite directions. Qis a decreasing function of P.
Demand: Q=Q(P)
Inverse demand: P=P(Q)
The higher the price, the
EMET1001
Foundations of Economic and Financial Models
Week 11: Matrix Algebra
Idione Meneghel
Australian National University
Spring 2016
Meneghel (ANU)
Week 11
Spring 2016
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Systems of linear equations (15.1)
Fundamental problem of linear algebra: s
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Multivariable Calculus Review
Idione Meneghel
Partial derivatives
Definition
Notation
For z = f (x, y), the partial derivative of f with re Equivalent notations:
spect to x at a poin
Tutorial Solutions: Week 5
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Note: These are only sketches of the solutions. Fully correct solutions require all
working and/or written explanation.
Review problems for chapter 8
Questi
EMET1001
Foundations of Economic and Financial Models
Week 2: Properties of functions
Idione Meneghel
Australian National University
Spring 2016
Meneghel (ANU)
Week 2
Spring 2016
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Shifting graph (5.1)
Suppose we know the function
f (x)
What can we
EMET1001: Foundations of Economic and Financial Models
Solutions for Practice Questions: Final Exam
Idione Meneghel
October, 2016.
1. Consider the following function
f (x) = x3 2x2 + x
(a) Find the domain of f .
(b) Compute the limit of f as x and x .
(c)
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Linear Algebra Review
Idione Meneghel
Linear equations and matrix algebra
Note 2: If A is an m n matrix, then Ax is a
vector in Rm , and it is the linear combination of the
columns of
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Mathematical Preliminaries
Idione Meneghel
Sets
Definition
Examples
A set A is a collection of objects (elements) such that
given any object x it is possible to determine whether
or n
Tutorial Assignment: Week 11
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Due: October 17 at 2pm
Note: These are the questions for the tutorial assignment taken from the textbook
Essential Mathematics for Economic Analysis. Each
EMETlOOl
Foundations of Economic and Financial Models
Week 9: Comparative Statics
ldione Meneghel
Australian National University
Spring 2016
Meneghel
(ANU)

Week 9
 

  
Spring 2016
1 / 33
A simple chain rule (12.1)
[T] The chain rule
If z = F(x,y)
Tutorial Solutions: Week 9
EMET1001: Foundations of Economic and Financial Models
Semester 2, 2016
Note: These are only sketches of the solutions. Fully correct solutions require all
working and/or written explanation.
Review problems for chapter 12
Quest